Finite element implementation of anisotropic quasi-linear viscoelasticity using a discrete spectrum approximation

Puso, M. A.; Weiss, J. A.

Affiliations

¹Methods Development Group, Lawrence Livermore National Laboratory, Livermore, CA 94550

²Orthopedic Biomechanics Institute, The Orthopedic Specialty Hospital, Salt Lake City, UT 84107

³Department of Bioengineering, University of Utah, Salt Lake City, UT 84112

Abstract and keywords

The objective of this work was to develop a theoretical and computational framework to apply the finite element method to anisotropic, viscoelastic soft tissues. The quasi-linear viscoelastic (QLV) theory provided the basis for the development. To allow efficient and easy computational implementation, a discrete spectrum approximation was developed for the QLV relaxation function. This approximation provided a graphic means to fit experimental data with an exponential series. A transversely isotropic hyperelastic material model developed for ligaments and tendons was used for the elastic response. The viscoelastic material model was implemented in a general-purpose, nonlinear finite element program. Test problems were analyzed to assess the performance of the discrete spectrum approximation and the accuracy of the finite element implementation. Results indicated that the formulation can reproduce the anisotropy and time-dependent material behavior observed in soft tissues. Application of the formulation to the analysis of the human femur-medial collateral ligament–tibia complex demonstrated the ability of the formulation to analyze large three-dimensional problems in the mechanics of biological joints.

Keywords:

Links

DOI: 10.1115/1.2834308

PubMed: 9675682

WoS: 000072307300011

History

Received: 1995-10-10

Revised: 1997-01-03

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